The generation of seismic images is used to determine subsurface geological features of interest in hydrocarbon exploration. Seismic imaging has been conventionally performed by causing a seismic disturbance on the surface, and recording seismic waves on each of a plurality of receivers strung along a shot line. Particularly in marine use, an air gun array is used as the wave source, and a trailing cable of hydrophone receivers which can be approximately 10,000 feet long are used to receive reflected waves. Each receiver records pressure wave amplitude as a function of time. These data are then used to assemble a graph or array of data in the (x,t) plane, with the x axis being coaxial with the shot line and the t axis representing the time in which reflection wave phenomena are received back at each receiver.
Using these data, traveltime profiles are built up in each (x,t) plane. Conventional processing techniques are used to transform these traveltime profiles in the (x,t) plane by seismic imaging into depth profiles in the (x,z) plane, where z denotes depth. The depth profiles ideally correspond to a geologic section taken along the same shot line.
The raw traveltime profile exhibits artifacts that distort the image. Among these are a shift in both the x direction and in the amount of slope of dipping reflectors, which are strata that slope downward in relation to the shot line. Other artifacts, known as diffraction hyperbolae, are created from prominent diffraction points. These artifacts make interpretation of the raw traveltime or depth profiles difficult or impossible.
Several techniques have been developed in the prior art for removing or reducing the strength of these artifacts such that a more interpretable depth or traveltime profiles may be obtained. Once such technique, known as migration, moves dipping reflectors into their true subsurface positions and collapses diffractions, thereby delineating detailed subsurface features such as fault planes. These migrations are commonly performed using a single shot line of data, such that one (x,z) depth profile will have increased spatial resolution. Such migrations are called 2-dimensional (2-D) migrations. One type of 2-D migration is the diffraction summation or Kirchhoff summation migration, and will be explained in more detail in the Detailed Description of the Invention below.
2-D migrations of data still do not produce completely valid images because (1) diffraction hyperbolae might be due to diffraction sources that lie outside of the (x,t) plane of the shot line data, and (2) the subsurface will generally dip in a direction other than one that is either parallel to (strike) or perpendicular to (in-line) the shot line. To solve this problem, 3-dimensional (3-D) migrations have been performed that use an array of data obtained from a regular array of parallel shot lines. If the migration velocity field does not have large lateral gradients, an excellent approximation to 3-D migration is obtained by performing 2-D migration along the lines parallel to the shot line data, and then along a series of lines perpendicular to the shot lines. A few hundred thousands to a few million traces are normally collected during a 3-D survey. This makes 3-D migrations based on new data extremely costly.
Many areas have been explored extensively over the years with 2-D seismic data. Often the available data forms a dense grid of irregularly oriented seismic lines having widely variable vintage. Several investigators have therefore attempted to conform irregular grids of 2-D data to a regular grid for subsequent input into a standard 3-D migration process. This is because practical techniques such as fine-difference or FK migrations require the input data to be uniformly sampled on a rectangular grid. To develop the rectangular grid, prior investigators have developed very elaborate, labor-intensive methods for interpolating the unmigrated stacked data from the available seismic lines onto a regular grid for subsequent input into a standard 3-D migration process. This interpolation is often very difficult, particularly since it must be performed on unmigrated data often having diffractions and crossing events which defy interpretive analysis.
A need has therefore arisen to find a migration algorithm which will accept the irregular grid of input data and produce a 3-D migrated output having uniform spatial sampling required for a 3-D interpretation. The Kirchhoff migration algorithm known in the art has just these features. Unfortunately, conventional applications of this method have been considered grossly impractical for 3-D processing because they require an enormous amount of input/output activity and CPU time.